Let X1 and X2 have joint density function given by fx1 x2 x

Let X1, and X2 have joint density function given by:
f(x1, x2) =     x1 + x2     0<x1<1.0 , 0 <x2<1.0
   0      otherwise

a. Find the marginal density function of X1 and X2.
b. Are X1 and X2 independent?c. Find the conditional density function of X1 given X2 = 0.5.d. Find correlation coefficient between X1 and X2

Solution

a) marginal density function of X1= integral f(X1,X2)dX2 limits from 0 to 1

=X1+1/2

similarly marginal density function for X2= X2+1/2

b)X1 and X2 are not independent since f(X1)xf(X2)!=f(X1,X2)

c)conditional density function of X1 given (X2=0.5) = integral f(X1|X2=0.5) limits from 0 to 1

=1/2+1/2=1

d)http://en.wikipedia.org/wiki/Correlation_and_dependence open this link and you will find the answer